Ulyanov-type Inequalities Between Lorentz–Zygmund Spaces
We establish inequalities of Ulyanov-type for moduli of smoothness relating the source Lorentz–Zygmund space L p , r ( log L ) α - γ , γ > 0 , and the target space L p ∗ , s ( log L ) α over R n if 1 < p < p ∗ < ∞ and over T n if 1 < p ≤ p ∗ < ∞ . The stronger logarithmic integrabi...
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| Veröffentlicht in: | The Journal of fourier analysis and applications 2014-10, Vol.20 (5), p.1020-1049 |
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| container_end_page | 1049 |
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| container_issue | 5 |
| container_start_page | 1020 |
| container_title | The Journal of fourier analysis and applications |
| container_volume | 20 |
| creator | Gogatishvili, Amiran Opic, Bohumír Tikhonov, Sergey Trebels, Walter |
| description | We establish inequalities of Ulyanov-type for moduli of smoothness relating the source Lorentz–Zygmund space
L
p
,
r
(
log
L
)
α
-
γ
,
γ
>
0
,
and the target space
L
p
∗
,
s
(
log
L
)
α
over
R
n
if
1
<
p
<
p
∗
<
∞
and over
T
n
if
1
<
p
≤
p
∗
<
∞
.
The stronger logarithmic integrability (corresponding to
L
p
∗
,
s
(
log
L
)
α
) is balanced by an additional logarithmic smoothness. |
| doi_str_mv | 10.1007/s00041-014-9343-4 |
| format | Article |
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L
p
,
r
(
log
L
)
α
-
γ
,
γ
>
0
,
and the target space
L
p
∗
,
s
(
log
L
)
α
over
R
n
if
1
<
p
<
p
∗
<
∞
and over
T
n
if
1
<
p
≤
p
∗
<
∞
.
The stronger logarithmic integrability (corresponding to
L
p
∗
,
s
(
log
L
)
α
) is balanced by an additional logarithmic smoothness.</description><identifier>ISSN: 1069-5869</identifier><identifier>EISSN: 1531-5851</identifier><identifier>DOI: 10.1007/s00041-014-9343-4</identifier><language>eng</language><publisher>Boston: Springer US</publisher><subject>Abstract Harmonic Analysis ; Algebra ; Analysis ; Approximations and Expansions ; Fourier Analysis ; Mathematical Methods in Physics ; Mathematics ; Mathematics and Statistics ; Numerical analysis ; Partial Differential Equations ; Signal,Image and Speech Processing</subject><ispartof>The Journal of fourier analysis and applications, 2014-10, Vol.20 (5), p.1020-1049</ispartof><rights>Springer Science+Business Media New York 2014</rights><rights>COPYRIGHT 2014 Springer</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c370t-18d886fab6fd7577ae59c73f638e33fc31e828a489c56268f73a41f7f7de2d6f3</citedby><cites>FETCH-LOGICAL-c370t-18d886fab6fd7577ae59c73f638e33fc31e828a489c56268f73a41f7f7de2d6f3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00041-014-9343-4$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00041-014-9343-4$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Gogatishvili, Amiran</creatorcontrib><creatorcontrib>Opic, Bohumír</creatorcontrib><creatorcontrib>Tikhonov, Sergey</creatorcontrib><creatorcontrib>Trebels, Walter</creatorcontrib><title>Ulyanov-type Inequalities Between Lorentz–Zygmund Spaces</title><title>The Journal of fourier analysis and applications</title><addtitle>J Fourier Anal Appl</addtitle><description>We establish inequalities of Ulyanov-type for moduli of smoothness relating the source Lorentz–Zygmund space
L
p
,
r
(
log
L
)
α
-
γ
,
γ
>
0
,
and the target space
L
p
∗
,
s
(
log
L
)
α
over
R
n
if
1
<
p
<
p
∗
<
∞
and over
T
n
if
1
<
p
≤
p
∗
<
∞
.
The stronger logarithmic integrability (corresponding to
L
p
∗
,
s
(
log
L
)
α
) is balanced by an additional logarithmic smoothness.</description><subject>Abstract Harmonic Analysis</subject><subject>Algebra</subject><subject>Analysis</subject><subject>Approximations and Expansions</subject><subject>Fourier Analysis</subject><subject>Mathematical Methods in Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Numerical analysis</subject><subject>Partial Differential Equations</subject><subject>Signal,Image and Speech Processing</subject><issn>1069-5869</issn><issn>1531-5851</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNp9kE1OwzAQRi0EEqVwAHa5gIsdO7bDrlT8VKrEArphYxlnXKVKnWInoLDiDtyQk-AqrNEs5tNo3kjzELqkZEYJkVeREMIpJpTjknGG-RGa0IJRXKiCHqdMRJmyKE_RWYxbQnLKJJug63UzGN--427YQ7b08Nabpu5qiNkNdB8APlu1AXz3-fP1_TJsdr2vsqe9sRDP0YkzTYSLvz5F67vb58UDXj3eLxfzFbZMkg5TVSklnHkVrpKFlAaK0krmBFPAmLOMgsqV4aq0hciFcpIZTp10soK8Eo5N0Wy8uzEN6Nq7tgvGpqpgV9vWg6vTfC6p4jmXQiaAjoANbYwBnN6HemfCoCnRB1t6tKWTLX2wpXli8pGJaddvIOht2wef_voH-gVXrG3I</recordid><startdate>20141001</startdate><enddate>20141001</enddate><creator>Gogatishvili, Amiran</creator><creator>Opic, Bohumír</creator><creator>Tikhonov, Sergey</creator><creator>Trebels, Walter</creator><general>Springer US</general><general>Springer</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20141001</creationdate><title>Ulyanov-type Inequalities Between Lorentz–Zygmund Spaces</title><author>Gogatishvili, Amiran ; Opic, Bohumír ; Tikhonov, Sergey ; Trebels, Walter</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c370t-18d886fab6fd7577ae59c73f638e33fc31e828a489c56268f73a41f7f7de2d6f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Abstract Harmonic Analysis</topic><topic>Algebra</topic><topic>Analysis</topic><topic>Approximations and Expansions</topic><topic>Fourier Analysis</topic><topic>Mathematical Methods in Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Numerical analysis</topic><topic>Partial Differential Equations</topic><topic>Signal,Image and Speech Processing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gogatishvili, Amiran</creatorcontrib><creatorcontrib>Opic, Bohumír</creatorcontrib><creatorcontrib>Tikhonov, Sergey</creatorcontrib><creatorcontrib>Trebels, Walter</creatorcontrib><collection>CrossRef</collection><jtitle>The Journal of fourier analysis and applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gogatishvili, Amiran</au><au>Opic, Bohumír</au><au>Tikhonov, Sergey</au><au>Trebels, Walter</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Ulyanov-type Inequalities Between Lorentz–Zygmund Spaces</atitle><jtitle>The Journal of fourier analysis and applications</jtitle><stitle>J Fourier Anal Appl</stitle><date>2014-10-01</date><risdate>2014</risdate><volume>20</volume><issue>5</issue><spage>1020</spage><epage>1049</epage><pages>1020-1049</pages><issn>1069-5869</issn><eissn>1531-5851</eissn><abstract>We establish inequalities of Ulyanov-type for moduli of smoothness relating the source Lorentz–Zygmund space
L
p
,
r
(
log
L
)
α
-
γ
,
γ
>
0
,
and the target space
L
p
∗
,
s
(
log
L
)
α
over
R
n
if
1
<
p
<
p
∗
<
∞
and over
T
n
if
1
<
p
≤
p
∗
<
∞
.
The stronger logarithmic integrability (corresponding to
L
p
∗
,
s
(
log
L
)
α
) is balanced by an additional logarithmic smoothness.</abstract><cop>Boston</cop><pub>Springer US</pub><doi>10.1007/s00041-014-9343-4</doi><tpages>30</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1069-5869 |
| ispartof | The Journal of fourier analysis and applications, 2014-10, Vol.20 (5), p.1020-1049 |
| issn | 1069-5869 1531-5851 |
| language | eng |
| recordid | cdi_gale_infotracacademiconefile_A718424767 |
| source | SpringerLink Journals |
| subjects | Abstract Harmonic Analysis Algebra Analysis Approximations and Expansions Fourier Analysis Mathematical Methods in Physics Mathematics Mathematics and Statistics Numerical analysis Partial Differential Equations Signal,Image and Speech Processing |
| title | Ulyanov-type Inequalities Between Lorentz–Zygmund Spaces |
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